Warm Up Activity Four 4s

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Warm Up ActivityFour 4s

• Use four 4s and the arithmetic operations (, -,
  x, /) plus grouping symbols to create each of the
  counting numbers from 0 to 10.
• Use exactly four 4s for each number.

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Counting

• Did humans always do math as we do it today?
• Did they always use the symbols we use?

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Numbers vs Numerals
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Early numbers

• Numbers did not start out as 1, 2, 3,
• The first numeration systems were often 1, 2,
  many. More complex number systems arose out of
  need.

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Numeration Systems

• Tally systems at a time.
• Egyptian--probably earliest known
• Babylonian--only two symbols
• Roman--most widespread, all over Europe from the
  Roman Empire
• Mayan--only three symbols
• Hindu-Arabic--what we use today

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Egyptian Numerals

• Used at about the same time as Babylonian
  Numbers--many similarities
• More symbols
• 1 10 100 1000 10,000
• More symbols for 100,000 and 1,000,000

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Egyptian Numeration

• 300 10 310 (Notice no ones)
• 20,000 300 4 20304

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Babylonian Numerals

• Initially, no zero. Later developed
• Two symbols only? 1 10.
• Additive when written from greatest to least
  ? ? ? 1010111
• Use 60 as a base--there is a break after 60.? ?
  ? ? means 606060101

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Babylonian Numeration

• ? ? ?
• 1 ____ 11 60 21
• 1 60 60 11 60 21
• 3600 660 21 4281

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Mayan Numerals

• Used the concept of zero, but only for place
  holders
• Used three symbols --- 1 5 0
• Wrote their numbers vertically is 3 5
  8, --- is 5 5 10

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Mayan Numeration

• New place value left a vertical gap.
• is one 20, and 0 ones 20.
• is two ___ 6

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Roman Numerals

• No zero.
• Symbols I 1, V 5, X 10, L 50, C 100,
  D 500, and M 1000
• If the Roman Numerals are in order from greatest
  to least, then addVII 5 1 1 7 XVI 10
  5 1 16

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Roman Numerals

• I 1, V 5, X 10, L 50, C 100, D 500,
  and M 1000.
• If the Roman numerals are NOT in order from
  greatest to least, then subtract where the order
  is wrong.IV 5 - 1 4 IX 10 - 1 XCII
  100 - 10 1 1 92

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Exploration 2.8

• Exploration 2.8--We will not do this entire
  thing--it is too long! But we will do parts.
  Today, we will begin with manipulatives.

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Alphabitia

• Read the introduction.
• Use the artifacts. Unit Long
• Flat

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Your job

• Create a numeration system for your tribe using
  the artifacts left by the member who died. Think
  about what features are desirable in a numeration
  system. Make notes, and be ready to explain it
  to others who are not part of this tribe. It
  should be logical, and be able to be continued
  past Z.
• Be ready to present your groups numeration
  system for the Alphabitians on Tuesday.

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Alphabitia Numeration System Proposals

• What did you come up with in your group?
• What are the pros and cons of your groups system
  and the other groups systems?